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  • 1. Agarwal, S.
    et al.
    Wettlaufer, J. S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, New Haven, CT, USA; Mathematical Institute, University of Oxford, Oxford, UK.
    Fluctuations in Arctic sea-ice extent: Comparing observations and climate models2018In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2129, article id 20170332Article in journal (Refereed)
    Abstract [en]

    The fluctuation statistics of the observed sea-ice extent during the satellite era are compared with model output from CMIP5 models using a multifractal time series method. The two robust features of the observations are that on annual to biannual time scales the ice extent exhibits white noise structure, and there is a decadal scale trend associated with the decay of the ice cover. It is shown that (i) there is a large inter-model variability in the time scales extracted from the models, (ii) none of the models exhibits the decadal time scales found in the satellite observations, (iii) five of the 21 models examined exhibit the observed white noise structure, and (iv) the multi-model ensemble mean exhibits neither the observed white noise structure nor the observed decadal trend. It is proposed that the observed fluctuation statistics produced by this method serve as an appropriate test bed for modelling studies. 

  • 2. Agarwal, Sahil
    et al.
    Del Sordo, Fabio
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    EXOPLANETARY DETECTION BY MULTIFRACTAL SPECTRAL ANALYSIS2017In: Astronomical Journal, ISSN 0004-6256, E-ISSN 1538-3881, Vol. 153, no 1, article id 12Article in journal (Refereed)
    Abstract [en]

    Owing to technological advances, the number of exoplanets discovered has risen dramatically in the last few years. However, when trying to observe Earth analogs, it is often difficult to test the veracity of detection. We have developed a new approach to the analysis of exoplanetary spectral observations based on temporal multifractality, which identifies timescales that characterize planetary orbital motion around the host star and those that arise from stellar features such as spots. Without fitting stellar models to spectral data, we show how the planetary signal can be robustly detected from noisy data using noise amplitude as a source of information. For observation of transiting planets, combining this method with simple geometry allows us to relate the timescales obtained to primary and secondary eclipse of the exoplanets. Making use of data obtained with ground-based and space-based observations we have tested our approach on HD 189733b. Moreover, we have investigated the use of this technique in measuring planetary orbital motion via Doppler shift detection. Finally, we have analyzed synthetic spectra obtained using the SOAP 2.0 tool, which simulates a stellar spectrum and the influence of the presence of a planet or a spot on that spectrum over one orbital period. We have demonstrated that, so long as the signal-to-noise-ratio >= 75, our approach reconstructs the planetary orbital period, as well as the rotation period of a spot on the stellar surface.

  • 3. Agarwal, Sahil
    et al.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Maximal stochastic transport in the Lorenz equations2016In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 380, no 1-2, p. 142-146Article in journal (Refereed)
    Abstract [en]

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  • 4. Agarwal, Sahil
    et al.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, United States; University of Oxford, United Kingdom.
    The Statistical Properties of Sea Ice Velocity Fields2017In: Journal of Climate, ISSN 0894-8755, E-ISSN 1520-0442, Vol. 30, no 13, p. 4873-4881Article in journal (Refereed)
    Abstract [en]

    By arguing that the surface pressure field over the Arctic Ocean can be treated as an isotropic, stationary, homogeneous, Gaussian random field, Thorndike estimated a number of covariance functions from two years of data (1979 and 1980). Given the active interest in changes of general circulation quantities and indices in the polar regions during the recent few decades, the spatial correlations in sea ice velocity fields are of particular interest. It is thus natural to ask, "How persistent are these correlations?'' To this end, a multifractal stochastic treatment is developed to analyze observed Arctic sea ice velocity fields from satellites and buoys for the period 1978-2015. Since it was previously found that the Arctic equivalent ice extent (EIE) has a white noise structure on annual to biannual time scales, the connection between EIE and ice motion is assessed. The long-term stationarity of the spatial correlation structure of the velocity fields and the robustness of their white noise structure on multiple time scales is demonstrated; these factors (i) combine to explain the white noise characteristics of the EIE on annual to biannual time scales and (ii) explain why the fluctuations in the ice velocity are proportional to fluctuations in the geostrophic winds on time scales of days to months. Moreover, it is shown that the statistical structure of these two quantities is commensurate from days to years, which may be related to the increasing prevalence of free drift in the ice pack.

  • 5.
    He, Andong
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Hertz beyond belief2014In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 10, no 13, p. 2264-2269Article in journal (Refereed)
    Abstract [en]

    We examine the validity of Hertz's linear elastic theory for central collisions of spheres using a viscoelastic model. This model explains why Hertz's theory is accurate in predicting the collision time and maximum contact area even when 40% of the kinetic energy is lost due to viscous dissipation. The main reason is that both the collision time and maximum contact area have a very weak dependence on the impact velocity. Moreover, we show that colliding objects exhibit an apparent size-dependent yield strength, which results from larger objects dissipating less energy at a given impact velocity.

  • 6. Lee, Alpha A.
    et al.
    Vella, Dominic
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Fluctuation spectra and force generation in nonequilibrium systems2017In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 114, no 35, p. 9255-9260Article in journal (Refereed)
    Abstract [en]

    Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The nonequilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that, for a narrow, unimodal spectrum, the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important nonequilibrium interactions are encoded within the fluctuation spectrum. In this sense, the noise becomes the signal.

  • 7. MacMinn, Christopher W.
    et al.
    Dufresne, Eric R.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Fluid-Driven Deformation of a Soft Granular Material2015In: Physical Review X, ISSN 2160-3308, E-ISSN 2160-3308, Vol. 5, no 1, article id 011020Article in journal (Refereed)
    Abstract [en]

    Compressing a porous, fluid-filled material drives the interstitial fluid out of the pore space, as when squeezing water out of a kitchen sponge. Inversely, injecting fluid into a porous material can deform the solid structure, as when fracturing a shale for natural gas recovery. These poromechanical interactions play an important role in geological and biological systems across a wide range of scales, from the propagation of magma through Earth's mantle to the transport of fluid through living cells and tissues. The theory of poroelasticity has been largely successful in modeling poromechanical behavior in relatively simple systems, but this continuum theory is fundamentally limited by our understanding of the pore-scale interactions between the fluid and the solid, and these problems are notoriously difficult to study in a laboratory setting. Here, we present a high-resolution measurement of injection-driven poromechanical deformation in a system with granular microsctructure: We inject fluid into a dense, confined monolayer of soft particles and use particle tracking to reveal the dynamics of the multiscale deformation field. We find that a continuum model based on poroelasticity theory captures certain macroscopic features of the deformation, but the particle-scale deformation field exhibits dramatic departures from smooth, continuum behavior. We observe particle-scale rearrangement and hysteresis, as well as petal-like mesoscale structures that are connected to material failure through spiral shear banding.

  • 8. MacMinn, Christopher W.
    et al.
    Dufresne, Eric R.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Large Deformations of a Soft Porous Material2016In: Physical Review Applied, ISSN 2331-7019, Vol. 5, no 4, article id 044020Article in journal (Refereed)
    Abstract [en]

    Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from cell and tissue mechanics to geomechanics and hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy's law with Terzaghi's effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. The well-known theory of large-deformation poroelasticity combines Darcy's law with Terzaghi's effective stress and nonlinear elasticity in a rigorous kinematic framework. This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues and in geomechanics to model large elastoplastic deformations in soils. Here, we first provide an overview and discussion of this theory with an emphasis on the physics of poromechanical coupling. We present the large-deformation theory in an Eulerian framework to minimize the mathematical complexity, and we show how this nonlinear theory simplifies to linear poroelasticity under the assumption of small strain. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of two uniaxial model problems: fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We explore the steady and dynamical errors associated with the linear model in both situations, as well as the impact of introducing a deformation-dependent permeability. We show that the error in linear poroelasticity is due primarily to kinematic nonlinearity and that this error (i) plays a surprisingly important role in the dynamics of the deformation and (ii) is amplified by nonlinear constitutive behavior, such as deformation-dependent permeability.

  • 9.
    Mancarella, Francesco
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Style, Robert W.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids2016In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 12, no 10, p. 2744-2750Article in journal (Refereed)
    Abstract [en]

    In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length L equivalent to gamma/E. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid interfacial stress when it is treated as an isotropic, strain-independent surface tension. Within this framework, the composite stiffness depends solely on the ratio of the elastocapillarity length L to the inclusion radius R. Independent of inclusion volume fraction, we find that the composite is stiffened by the inclusions whenever R < 3L/2. Over the same range of parameters, we compare our results with alternative approaches (dilute and Mori-Tanaka theories that include surface tension). Our framework can be easily extended to calculate the composite properties of more general soft materials where surface tension plays a role.

  • 10.
    Mancarella, Francesco
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden; Yale University, United States; University of Oxford, United Kingdom.
    Surface tension and a self-consistent theory of soft composite solids with elastic inclusions2017In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 13, no 5, p. 945-955Article in journal (Refereed)
    Abstract [en]

    The importance of surface tension effects is being recognized in the context of soft composite solids, where they are found to significantly affect the mechanical properties, such as the elastic response to an external stress. It has recently been discovered that Eshelby's inclusion theory breaks down when the inclusion size approaches the elastocapillary length L ≡ γ/E, where γ is the inclusion/host surface tension and E is the host Young's modulus. Extending our recent results for liquid inclusions, here we model the elastic behavior of a non-dilute distribution of isotropic elastic spherical inclusions in a soft isotropic elastic matrix, subject to a prescribed infinitesimal far-field loading. Within our framework, the composite stiffness is uniquely determined by the elastocapillary length L, the spherical inclusion radius R, and the stiffness contrast parameter C, which is the ratio of the inclusion to the matrix stiffness. We compare the results with those from the case of liquid inclusions, and we derive an analytical expression for elastic cloaking of the composite by the inclusions. Remarkably, we find that the composite stiffness is influenced significantly by surface tension even for inclusions two orders of magnitude more stiff than the host matrix. Finally, we show how to simultaneously determine the surface tension and the inclusion stiffness using two independent constraints provided by global and local measurements.

  • 11.
    Marath, Navaneeth K.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, S-10691 Stockholm, Sweden..
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, S-10691 Stockholm, Sweden.;Yale Univ, New Haven, CT 06520 USA..
    Hydrodynamic interactions and the diffusivity of spheroidal particles2019In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 151, no 2, article id 024107Article in journal (Refereed)
    Abstract [en]

    It is intuitive that the diffusivity of an isolated particle differs from those in a monodisperse suspension, in which hydrodynamic interactions between the particles are operative. Batchelor [J. Fluid Mech. 74, 1-29 (1976) and J. Fluid Mech. 131, 155-175 (1983)] calculated how hydrodynamic interactions influenced the diffusivity of a dilute suspension of spherical particles, and Russel et al. [Colloidal Dispersions (Cambridge University Press, 1991)] and Brady [J. Fluid Mech. 272, 109-134 (1994)] treated nondilute (higher particle volume fraction) suspensions. Although most particles lack perfect sphericity, little is known about the effects of hydrodynamic interactions on the diffusivity of spheroidal particles, which are the simplest shapes that can be used to model anisotropic particles. Here, we calculate the effects of hydrodynamic interactions on the translational and rotational diffusivities of spheroidal particles of arbitrary aspect ratio in dilute monodisperse suspensions. We find that the translational and rotational diffusivities of prolate spheroids are more sensitive to eccentricity than for oblate spheroids. The origin of the hydrodynamic anisotropy is that found in the stresslet field for the induced-dipole interaction. However, in the dilute limit, the effects of anisotropy are at the level of a few percent. These effects have influence on a vast range of settings, from partially frozen colloidal suspensions to the dynamics of cytoplasm.

  • 12.
    Mitra, Dhrubaditya
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Can planetesimals form by collisional fusion?2013In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 773, no 2, p. 120-Article in journal (Refereed)
    Abstract [en]

    As a test bed for the growth of protoplanetary bodies in a turbulent circumstellar disk, we examine the fate of a boulder using direct numerical simulations of particle seeded gas flowing around it. We provide an accurate description of the flow by imposing no-slip and non-penetrating boundary conditions on the boulder surface using the immersed boundary method pioneered by Peskin. Advected by the turbulent disk flow, the dust grains collide with the boulder and we compute the probability density function of the normal component of the collisional velocity. Through this examination of the statistics of collisional velocities, we test the recently developed concept of collisional fusion which provides a physical basis for a range of collisional velocities exhibiting perfect sticking. A boulder can then grow sufficiently rapidly to settle into a Keplerian orbit on disk evolution timescales.

  • 13. Moon, W.
    et al.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, United States.
    A stochastic dynamical model of arctic sea ice2017In: Journal of Climate, ISSN 0894-8755, E-ISSN 1520-0442, Vol. 30, no 13, p. 5119-5140Article in journal (Refereed)
    Abstract [en]

    The noise forcing underlying the variability in the Arctic ice cover has a wide range of principally unknown origins. For this reason, the analytical and numerical solutions of a stochastic Arctic sea ice model are analyzed with both additive and multiplicative noise over a wide range of external heat fluxes ΔF0, corresponding to greenhouse gas forcing. The stochastic variability fundamentally influences the nature of the deterministic steady-state solutions corresponding to perennial and seasonal ice and ice-free states. Thus, the results are particularly relevant for the interpretation of the state of the system as the ice cover thins with ΔF0, allowing a thorough examination of the differing effects of additive versus multiplicative noise. In the perennial ice regime, the principal stochastic moments are calculated and compared to those determined from a stochastic perturbation theory described previously. As ΔF0 increases, the competing contributions to the variability of the destabilizing sea ice-albedo feedback and the stabilizing longwave radiative loss are examined in detail. At the end of summer the variability of the stochastic paths shows a clear maximum, which is due to the combination of the increasing influence of the albedo feedback and an associated "memory effect," in which fluctuations accumulate from early spring to late summer. This is counterbalanced by the stabilization of the ice cover resulting from the longwave loss of energy from the ice surface, which is enhanced during winter, thereby focusing the stochastic paths and decreasing the variability. Finally, common examples in stochastic dynamics with multiplicative noise are discussed wherein the choice of the stochastic calculus (Itô or Stratonovich) is not necessarily determinable a priori from observations alone, which is why both calculi are treated on equal footing herein.

  • 14. Moon, W.
    et al.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    A unified nonlinear stochastic time series analysis for climate science2017In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, article id 44228Article in journal (Refereed)
    Abstract [en]

    Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.

  • 15.
    Moon, Woosok
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.;Stockholm Univ, S-10691 Stockholm, Sweden..
    Agarwal, Sahil
    Yale Univ, New Haven, CT 06520 USA..
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, S-10691 Stockholm, Sweden.;Yale Univ, New Haven, CT 06520 USA.;Univ Oxford, Math Inst, Oxford OX2 6GG, England..
    Intrinsic Pink-Noise Multidecadal Global Climate Dynamics Mode2018In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 121, no 10, article id 108701Article in journal (Refereed)
    Abstract [en]

    Understanding multidecadal variability is an essential goal of climate dynamics. For example, the recent phenomenon referred to as the "global warming hiatus" may reflect a coupling to an intrinsic, preindustrial, multidecadal variability process. Here, using a multifractal time-series method, we demonstrate that 42 data sets of 79 proxies with global coverage exhibit pink-noise characteristics on multidecadal timescales. To quantify the persistence of this behavior, we examine high-resolution ice core and speleothem data to find pink noise in both pre- and postindustrial periods. We examine the spatial structure with an empirical orthogonal function analysis of the monthly averaged surface temperature from 1901 to 2012. The first mode clearly shows the distribution of ocean heat flux sinks located in the eastern Pacific and the Southern Ocean and has pink-noise characteristics on a multidecadal timescale. We hypothesize that this pink-noise multidecadal spatial mode may resonate with externally driven greenhouse gas forcing, driving large-scale climate processes.

  • 16. Pramanik, S
    et al.
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Confinement effects in premelting dynamics2017In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 5, article id 052801Article in journal (Refereed)
    Abstract [en]

    We examine the effects of confinement on the dynamics of premelted films driven by thermomolecular pressure gradients. Our approach is to modify a well-studied setting in which the thermomolecular pressure gradient is driven by a temperature gradient parallel to an interfacially premelted elastic wall. The modification treats the increase in viscosity associated with the thinning of films, studied in a wide variety of materials, using a power law and we examine the consequent evolution of the confining elastic wall. We treat (1) a range of interactions that are known to underlie interfacial premelting and (2) a constant temperature gradient wherein the thermomolecular pressure gradient is a constant. The difference between the cases with and without the proximity effect arises in the volume flux of premelted liquid. The proximity effect increases the viscosity as the film thickness decreases thereby requiring the thermomolecular pressure driven flux to be accommodated at higher temperatures where the premelted film thickness is the largest. Implications for experiment and observations of frost heave are discussed.

  • 17.
    Pramanik, Satyajit
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, S-10691 Stockholm, Sweden..
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, S-10691 Stockholm, Sweden.;Yale Univ, New Haven, CT 06520 USA.;Univ Oxford, Math Inst, Oxford OX2 6GG, England..
    Confinement- induced control of similarity solutions in premelting dynamics and other thin film problems2019In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, no 3, p. 938-958Article in journal (Refereed)
    Abstract [en]

    We study the combined effects of nonlocal elasticity and confinement-induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement-induced ordering is modeled using a film thickness dependent viscosity. When there is no confinement-induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an in finite sequence of oscillations. However, when the confinement-induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations and similarity solutions vanish. Implications of our results for general thermomechanical dynamics, frost heave observations, and cryogenic cell preservation are discussed. Finally, through its influence on the viscosity, the confinement effect implicitly introduces a new universal length scale into the volume flux. Thus, there are a host of thin film problems, from droplet breakup to wetting/dewetting dynamics, whose properties (similarity solutions, regularization, and compact support) will change under the action of the confinement effect. Therefore, our study suggests revisiting the mathematical structure and experimental implications of a wide range of problems within the framework of the confinement effect.

  • 18. Schollick, Julia M. H.
    et al.
    Style, Robert W.
    Curran, Arran
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Dufresne, Eric R.
    Warren, Patrick B.
    Velikov, Krassimir P.
    Dullens, Roel P. A.
    Aarts, Dirk G. A. L.
    Segregated Ice Growth in a Suspension of Colloidal Particles2016In: Journal of Physical Chemistry B, ISSN 1520-6106, E-ISSN 1520-5207, Vol. 120, no 16, p. 3941-3949Article in journal (Refereed)
    Abstract [en]

    We study the freezing of a dispersion of colloidal silica particles in water, focusing on the formation of segregated ice in the form of ice lenses. Local temperature measurements in combination with video microscopy give insight into the rich variety of factors that control ice lens formation. We observe the initiation of the lenses, their growth morphology, and their final thickness and spacing over a range of conditions, in particular the effect of the particle packing and the cooling rate. We find that increasing the particle density drastically reduces the thickness of lenses but has little effect on the lens spacing. Therefore, the fraction of segregated ice formed reduces. The effect of the cooling rate, which is the product of the temperature gradient and the pulling speed across the temperature gradient, depends on which parameter is varied. A larger temperature gradient causes ice lenses to be initiated more frequently, while a lower pulling speed allows for more time for ice lenses to grow: both increase the fraction of segregated ice. Surprisingly, we find that the growth rate of a lens does not depend on its undercooling. Finally, we have indications of pore ice in front of the warmest ice lens, which has important consequences for the interpretation of the measured trends. Our findings are relevant for ice segregation occurring in a wide range of situations, ranging from model lab experiments and theories to geological and industrial processes, like frost heave and frozen food production.

  • 19. Style, Robert W.
    et al.
    Boltyanskiy, Rostislav
    Allen, Benjamin
    Jensen, Katharine E.
    Foote, Henry P.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale Univ, New Haven, USA.
    Dufresne, Eric R.
    Stiffening solids with liquid inclusions2015In: Nature Physics, ISSN 1745-2473, E-ISSN 1745-2481, Vol. 11, no 1, p. 82-87Article in journal (Refereed)
    Abstract [en]

    From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and synthetic materials. Eshelby's inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a composite's bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelby's theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated droplet's deformation is strongly size-dependent, with the smallest droplets mimicking the behaviour of solid inclusions. Furthermore, in opposition to the predictions of conventional composite theory, we find that finite concentrations of small liquid inclusions enhance the stiffness of soft solids. A straightforward extension of Eshelby's theory, accounting for the surface tension of the solid-liquid interface, explains our experimental observations. The counterintuitive stiffening of solids by fluid inclusions is expected whenever inclusion radii are smaller than an elastocapillary length, given by the ratio of the surface tension to Young's modulus of the solid matrix. These results suggest that surface tension can be a simple and effective mechanism to cloak the far-field elastic signature of inclusions.

  • 20. Style, Robert W.
    et al.
    Che, Yonglu
    Park, Su Ji
    Weon, Byung Mook
    Je, Jung Ho
    Hyland, Callen
    German, Guy K.
    Power, Michael P.
    Wilen, Larry A.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Dufresne, Eric R.
    Patterning droplets with durotaxis2013In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 110, no 31, p. 12541-12544Article in journal (Refereed)
    Abstract [en]

    Numerous cell types have shown a remarkable ability to detect and move along gradients in stiffness of an underlying substrate-a process known as durotaxis. The mechanisms underlying durotaxis are still unresolved, but generally believed to involve active sensing and locomotion. Here, we show that simple liquid droplets also undergo durotaxis. By modulating substrate stiffness, we obtain fine control of droplet position on soft, flat substrates. Unlike other control mechanisms, droplet durotaxis works without imposing chemical, thermal, electrical, or topographical gradients. We show that droplet durotaxis can be used to create large-scale droplet patterns and is potentially useful for many applications, such as microfluidics, thermal control, and microfabrication.

  • 21. Style, Robert W.
    et al.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, United States; University of Oxford, United Kingdom .
    Dufresne, Eric R.
    Surface tension and the mechanics of liquid inclusions in compliant solids2015In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 11, no 4, p. 672-679Article in journal (Refereed)
    Abstract [en]

    Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounting for the bulk elasticity of the solid and the surface tension (i.e. isotropic strain-independent surface stress) of the solid-liquid interface. Surface tension significantly alters the inclusion's shape and stiffness as well as its near-and far-field stress fields. These phenomena depend strongly on the ratio of the inclusion radius, R, to an elastocapillary length, L. Surface tension is significant whenever inclusions are smaller than 100L. While Eshelby theory predicts that liquid inclusions generically reduce the stiffness of an elastic solid, our results show that liquid inclusions can actually stiffen a solid when R < 3L/2. Intriguingly, surface tension cloaks the far-field signature of liquid inclusions when R = 3L/2. These results are have far-reaching applications from measuring local stresses in biological tissue, to determining the failure strength of soft composites.

  • 22.
    Toppaladoddi, S.
    et al.
    Univ Oxford, Oxford OX2 6GG, England.;Yale Univ, New Haven, CT 06520 USA..
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    The combined effects of shear and buoyancy on phase boundary stability2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 868, p. 648-665Article in journal (Refereed)
    Abstract [en]

    We study the effects of externally imposed shear and buoyancy driven flows on the stability of a solid-liquid interface. A linear stability analysis of shear and buoyancy-driven flow of a melt over its solid phase shows that buoyancy is the only destabilizing factor and that the regime of shear flow here, by inhibiting vertical motions and hence the upward heat flux, stabilizes the system. It is also shown that all perturbations to the solid-liquid interface decay at a very modest shear flow strength. However, at much larger shear-flow strength, where flow instabilities coupled with buoyancy might enhance vertical motions, a re-entrant instability may arise.

  • 23. Toppaladoddi, Srikanth
    et al.
    Succi, Sauro
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Roughness as a Route to the Ultimate Regime of Thermal Convection2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 118, no 7, article id 074503Article in journal (Refereed)
    Abstract [en]

    We use highly resolved numerical simulations to study turbulent Rayleigh-Benard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr = 1 and Ra = [4 x 10(6), 3 x 10(9)]. By varying the wavelength. at a fixed amplitude, we find an optimal wavelength lambda(opt) for which the Nusselt-Rayleigh scaling relation is (Nu - 1 proportional to Ra-0.483), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech. 804, 370 (2016)] who prove that Nu can grow no faster than O(Ra-1/2) as Ra -> infinity, and thus with the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When lambda << lambda(opt) and lambda >> lambda(opt), the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each Ra, we choose the maximum Nu among all., thus optimizing over all lambda, to find Nu(opt) - 1 = 0.01xRa(0.444).

  • 24. Toppaladoddi, Srikanth
    et al.
    Succi, Sauro
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, United States; University of Oxford, United Kingdom.
    Tailoring boundary geometry to optimize heat transport in turbulent convection2015In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 111, no 4, article id 44005Article in journal (Refereed)
    Abstract [en]

    By tailoring the geometry of the upper boundary in turbulent Rayleigh-Benard convection we manipulate the boundary layer-interior flow interaction, and examine the heat transport using the lattice Boltzmann method. For fixed amplitude and varying boundary wavelength., we find that the exponent beta in the Nusselt-Rayleigh scaling relation, Nu - 1 proportional to Ra-beta, is maximized at lambda =lambda(max) approximate to ( 2 pi)(-1), but decays to the planar value in both the large (lambda >> lambda(max)) and small (lambda << lambda(max)) wavelength limits. The changes in the exponent originate in the nature of the coupling between the boundary layer and the interior flow. We present a simple scaling argument embodying this coupling, which describes the maximal convective heat flux.

  • 25. Toppaladoddi, Srikanth
    et al.
    Wettlaufer, J. S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution2017In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 167, no 3-4, p. 683-702Article in journal (Refereed)
    Abstract [en]

    We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14): 148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker-Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106: 28-32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045): 20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e. g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, Delta F-0, increases. The mean ice thickness decays exponentially with Delta F-0, but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.

  • 26.
    Toppaladoddi, Srikanth
    et al.
    Yale Univ, New Haven, CT 06520 USA.;Univ Oxford, All Souls Coll, Oxford OX1 4AL, England.;Univ Oxford, Dept Phys, Oxford OX1 3PU, England.;Univ Oxford, Math Inst, Oxford OX2 6GG, England..
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale Univ, New Haven, CT 06520 USA.;Univ Oxford, Math Inst, Oxford OX2 6GG, England.
    Penetrative convection at high Rayleigh numbers2018In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 3, no 4, article id 043501Article in journal (Refereed)
    Abstract [en]

    We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is Ra = [10(6),10(8)] and the Prandtl numbers are Pr = 1 and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, Lambda, which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of Lambda denote increased stability of the upper stable layer. We study the effects of Lambda on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range Lambda = [0.01,4], we find that for a fixed Ra the Nusselt number, Nu, increases with decreasing Lambda. We also investigate the effects of Lambda on the vertical variation of convective heat flux and the Brunt-Vaisala frequency. Our results clearly indicate that in the limit Lambda -> 0 the problem reduces to that of the classical Rayleigh-Benard convection.

  • 27. Toppaladoddi, Srikanth
    et al.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Theory of the Sea Ice Thickness Distribution2015In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 115, no 14, article id 148501Article in journal (Refereed)
    Abstract [en]

    We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution g(h) from Thorndike et al. into a Fokker-Planck-like conservation law. The steady solution is g(h) = N(q)h(q)e(-h/H), where q and H are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for h << 1, g(h) is controlled by both thermodynamics and mechanics, whereas for h >> 1 only mechanics controls g(h). Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness h, from which we predict the observed g(h). The genericity of our approach provides a framework for studying the geophysical-scale structure of the ice pack using methods of broad relevance in statistical mechanics.

  • 28. Weady, S.
    et al.
    Agarwal, S.
    Wilen, L.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, New Haven, United States.
    Circuit bounds on stochastic transport in the Lorenz equations2018In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 382, no 26, p. 1731-1737Article in journal (Refereed)
    Abstract [en]

    In turbulent Rayleigh–Bénard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by the Rayleigh number. In experiments, one measures the Nusselt number for a given Rayleigh number, and the question of how close that value is to the maximal transport is a key prediction of variational fluid mechanics in the form of an upper bound. The Lorenz equations have traditionally been studied as a simplified model of turbulent Rayleigh–Bénard convection, and hence it is natural to investigate their upper bounds, which has previously been done numerically and analytically, but they are not as easily accessible in an experimental context. Here we describe a specially built circuit that is the experimental analogue of the Lorenz equations and compare its output to the recently determined upper bounds of the stochastic Lorenz equations [1]. The circuit is substantially more efficient than computational solutions, and hence we can more easily examine the system. Because of offsets that appear naturally in the circuit, we are motivated to study unique bifurcation phenomena that arise as a result. Namely, for a given Rayleigh number, we find a reentrant behavior of the transport on noise amplitude and this varies with Rayleigh number passing from the homoclinic to the Hopf bifurcation.

  • 29.
    Wettlaufer, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Surface phase transitions in ice: From fundamental interactions to applications2019In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 377, no 2146, article id 20180261Article in journal (Refereed)
    Abstract [en]

    Interfaces divide all phases of matter and yet in most practical settings it is tempting to ignore their energies and the associated implications. There are many reasons for this, not the least of which is the introduction of a new pair of canonically conjugate variables-interfacial energy and its counterpart the surface area. A key set of questions surrounding the treatment of multiphase flows concerns how and when we must account for such effects. I begin this discussion with an abbreviated review of the basic theory of lower-dimensional phase transitions and describe a range of situations in which the bulk behaviour of a two-phase (and in some cases twocomponent) system is dominated by surface effects. Then I discuss a number of settings in which the bulk and surface behaviour can interact on equal footing. These can include the dynamic and thermodynamic behaviour of floating sea ice, the freezing and drying of colloidal suspensions (such as soil) and the mechanisms of protoplanetesimal formation by inter-particle collisions in accretion discs. This article is part of the theme issue 'The physics and chemistry of ice: Scaffolding across scales, from the viability of life to the formation of planets'. © 2019 Royal Society Publishing. All rights reserved.

  • 30.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, United States; University of Oxford, United Kingdom.
    Climate Science: An invitation for physicists2016In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 116, no 15, article id 150002Article in journal (Refereed)
1 - 30 of 30
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